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螺面


Gyroid

如上圖所示,螺面是由 Schoen (1970) 發現的無限連通的週期性極小曲面,不包含直線(Osserman 1986)。Große-Brauckmann 和 Wohlgemuth (1996) 證明了螺面是嵌入的。

螺面是唯一已知的具有三重連線的嵌入式三週期極小曲面。此外,與 Anderson 等人 (1990) 研究的五個三週期極小曲面不同,螺面沒有任何反射對稱性 (Große-Brauckmann 1997)。

Gyroid metal sculpture (Bathsheba Grossman)

上面的影像展示了數字雕塑家 Bathsheba Grossman (http://www.bathsheba.com/) 建立的螺面金屬列印作品。


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極小曲面

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參考文獻

Anderson, D. M.; Davis, H. T.; Nitsche, J. C. C.; and Scriven, L. E. Adv. Chem. Phys. 77, 337-396, 1990.Garstecki, P. and Hołyst, R. "Scattering Patterns of Self-Assembled Gyroid Cubic Phases in Amphiphilic Systems." J. Chem. Phys. 115, 1095-1099, 2001.Gòzdz, W. and Hołyst, R. "High Genus Periodic Gyroid Surfaces of Nonpositive Gaussian Curvature." Phys. Rev. Lett. 76, 2726-2729, 1996.Große-Brauckmann, K. "Gyroids of Constant Mean Curvature." Experiment. Math. 6, 33-50, 1997.Große-Brauckmann, K. and Wohlgemuth, M. "The Gyroid Is Embedded and Has Constant Mean Curvature Companions." Calc. Var. Partial Differential Equations 4, 499-523, 1996.Grossman, B. "The Gyroid." http://www.bathsheba.com/math/gyroid/.Hyde, S. T.; Andersson, S.; Ericsson, B.; and Larsson, K. "A Cubic Structure Consisting of a Lipid Bilayer Forming an Infinite Periodic Minimal Surface of the Gyroid Type in the Glycerolmonooleate Water System." Z. Kristallogr. 168, 213-219, 1984.Hyde, S. T.; Andersson, S.; Blum, Z.; Lidin, S.; Larsson, K.; Landh, T.; and Ninham, B. W. The Language of Shape. Amsterdam, Netherlands: Elsevier, 1997.Mackay, A. L. "Periodic Minimal Surfaces." Nature 314, 604-606, 1985.Osserman, R. Frontispiece to A Survey of Minimal Surfaces. New York: Dover, 1986.Schoen, A. H. "Infinite Periodic Minimal Surfaces Without Selfintersections." NASA Tech. Note No. D-5541. Washington, DC, 1970.Terrones, H. "Computation of Minimal Surfaces." J. de Physique 51, No. 23, Suppl. Colloq. C7, 345-362, 1990.

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螺面

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Weisstein, Eric W. "螺面。" 來自 Web 資源。 https://mathworld.tw/Gyroid.html

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